Question

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$
(ii) $100x-x=17.\overline{18}$
(iii) $99x=18$

Answer 1

The simplest way of representing a simple fraction is by eliminating the recurring decimal. This can be done by a multiplying factor which can be $10$ or $100$ or any other number depending on the number of recurring digits.

$x=0.\overline{18}$ ....(I)

$100x=18.\overline{18}$ (multiplied by $100$ because there are only two repeating digits) ….(II)

Subtracting (I) from (II),

$99x=18$

Hence, the correct combinations are (i) and (iii).